Really depends on your problem, but in practice, the answer is usually "no".
If you could do it, we'd already have SETI like networks for AI.
Most modern large models cannot be trained on one instance of anything (GPU, accelerators, whatever), so there's no alternative to distributed training. They also wouldn't even fit in the memory of one GPU/accelerator, so there are even more complex ways to split the model across instances.
You can't scale averaging parallel runs much. You need to munch through evolutions/iterations fast.
You can't ie. start with random state, schedule parallel training averaging it all out and expect that you end up with well trained network in one step.
Every next step invalidates input state for everything and the state is gigantic.
It's dominated by huge transfers at high frequency.
You can't for example have 2x gpus connected with network cable and expect speedup. You need to put them on the same motherboard to have any gains.
SETI for example is unlike that - it can be easily distributed - partial readonly snapshot, intense computation, thin result submission.
The question was:
> > There is probably a simple answer to this question, but why isn't it possible to use a decentralized architecture like in crypto mining to train models?
> Can you copy a neural network, train each copy on a different part of the dataset, and merge them back together somehow?
The answer is flat out no.
It doesn't mean parallel computation doesn't happen. Everything, including single gpu, is massively parallel computation.
Does copying happen? Yes, but it's short lived and dominates, ie. data transfer is bottleneck and they go out of their ways to avoid it.
Distributing training in decentralized architecture fashion is not possible.
The lack of superposition means you can't efficiently train one layer separately from the others either.
That being said, a popular non-linear function in modern neural nets is ReLU[2] which is piece-wise linear, so perhaps there's some cleverness one can do there.
[1]: https://en.wikipedia.org/wiki/Superposition_principle
[2]: https://en.wikipedia.org/wiki/Rectifier_(neural_networks)